Senate Democrats joined Republicans Friday on a key procedural vote to advance a bill that would ultimately avert a government shutdown at midnight, despite intensifying pressure from across the Democratic Party to block the GOP’s funding measure.

While conservative House Republicans have in the past dug in and opposed such spending bills, forcing Mr. Johnson to rely on Democrats to keep the government open, President Trump called on Republicans to unite and push this measure through so he and Republicans on Capitol Hill could focus on their new budgetary and tax-cutting plans.